My question is, why use so many F-style clamps rather than just 3-4 parallel bar clamps that would cover the entire surface?
Probably the simplest explanation is to spread the clamping force more uniformly. Although this can be done using fewer larger clamps too, with use of clamping blocks, which appear to be in the photograph anyway.
Side note: I glued some 2-3/4" x 5-1/4" pieces together a few nights ago, and had a bit of trouble getting them to stay lined up while I tightened my K-Body style clamps on them. Would the F-style clamps have been easier to achieve a good alignment?
With conventional clamps of any kind keeping alignment can be tricky because so many woodworking glues lubricate the joint surfaces so well. Really it's not a matter of what clamp to use that prevents the problem but a clamping process or procedure that'll counteract it, or modifying the joint to maintain its own alignment: more traditional options including dowels and a long floating tenon (spline), and more recently biscuits.
Another option is to use cauls of some kind to physically hold the glue-up firmly flat, basically by clamping downwards across the boards as well as across the main clamping axis:
One final option that isn't as commonly seen it to build a clamping apparatus of some kind — a jig or clamping frame — that includes within it in some means to hold the glue-up flat, as in this example: